{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T13:20:32Z","timestamp":1768483232975,"version":"3.49.0"},"reference-count":27,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2023,9,15]],"date-time":"2023-09-15T00:00:00Z","timestamp":1694736000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"CNES"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>UAVs represent a tremendous opportunity to perform geophysical and repeated experiments, particularly in volcanic contexts. Their ability to be deployed rapidly and fly at various altitudes and the fact that they are easy to operate despite complex field conditions make them attractive for magnetic surveys. Detailed maps of the magnetic field in turn bring key constraints on the rocks\u2019 composition, thermal anomalies, intrusive systems, and crustal contrast evolution. Yet, raw magnetic field measurements require careful processing to minimize directional, positional, and crossover errors. Moreover, stitching together adjacent or overlapping surveys acquired at different times and altitudes is not a trivial task. Therefore, it is challenging in remote areas to directly evaluate the consistency of a survey and to ascertain the success of the field mission. In this paper, we present a fast algorithm allowing for a quick-look modeling of scalar magnetic intensity measurements. The approach relies on rectangular harmonic analysis (RHA). The field measurements are automatically corrected for a global main field. Then, they are projected along this main field and modeled in terms of RHA functions. The software can exploit the quality indices provided with data and a procedure is applied to mitigate the effect of outliers. Maps for the scalar and the vector anomaly fields are readily built on an interpolated regular grid leveled at a constant altitude. In order to assess the modeling and the inversion procedures, analyses are carried out with synthetic measurements derived from a high-resolution global lithospheric magnetic field model estimated on the French aeromagnetic grid and at UAV locations with some added nonrandom noise. These analyses indicate that RHA is efficient for first-order and direct mapping of the crustal magnetic field structures measured by UAVs but that it could be applied on airborne and marine magnetic intensity data covering dense and large geographical extensions.<\/jats:p>","DOI":"10.3390\/rs15184549","type":"journal-article","created":{"date-parts":[[2023,9,17]],"date-time":"2023-09-17T23:32:27Z","timestamp":1694993547000},"page":"4549","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A Quick-Look Software for In Situ Magnetic Field Modeling from Onboard Unmanned Aircraft Vehicles (UAVs) Measurements"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7038-2855","authenticated-orcid":false,"given":"Erwan","family":"Thebault","sequence":"first","affiliation":[{"name":"Laboratoire Magmas et Volcans, OPGC, IRD, CNRS, Universit\u00e9 Clermont Auvergne, 63000 Clermont-Ferrand, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8132-2428","authenticated-orcid":false,"given":"Lydie-Sarah","family":"Gailler","sequence":"additional","affiliation":[{"name":"Laboratoire Magmas et Volcans, OPGC, IRD, CNRS, Universit\u00e9 Clermont Auvergne, 63000 Clermont-Ferrand, France"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1285","DOI":"10.1007\/s10712-020-09611-7","article-title":"Geoscientists in the sky: Unmanned aerial vehicles responding to geohazards","volume":"41","author":"Antoine","year":"2020","journal-title":"Surv. Geophys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/B978-044452748-6\/00087-0","article-title":"The present field","volume":"5","author":"Hulot","year":"2007","journal-title":"Treatise Geophys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/s11214-016-0285-9","article-title":"Challenges handling magnetospheric and ionospheric signals in internal geomagnetic field modelling","volume":"206","author":"Finlay","year":"2017","journal-title":"Space Sci. Rev."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Zheng, Y., Li, S., Xing, K., and Zhang, X. (2021). Unmanned aerial vehicles for magnetic surveys: A review on platform selection and interference suppression. Drones, 5.","DOI":"10.3390\/drones5030093"},{"key":"ref_5","unstructured":"Schott, J.J., and Th\u00e9bault, E. (2010). Geomagnetic Observations and Models, Springer."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3021","DOI":"10.1029\/JB086iB04p03021","article-title":"Rectangular harmonic analysis applied to the geomagnetic field","volume":"86","author":"Alldredge","year":"1981","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1029\/TE050i001p00001","article-title":"Analysis and interpretation of geomagnetic anomalies","volume":"50","author":"Vestine","year":"1945","journal-title":"Terr. Magn. Atmos. Electr."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"829","DOI":"10.1190\/1.1439658","article-title":"Two-dimensional harmonic analysis as a tool for magnetic interpretation","volume":"30","author":"Bhattacharyya","year":"1965","journal-title":"Geophysics"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1921","DOI":"10.1029\/JB087iB03p01921","article-title":"Geomagnetic local and regional harmonic analyses","volume":"87","author":"Alldredge","year":"1982","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1001","DOI":"10.5636\/jgg.42.1001","article-title":"Regional Magnetic Field Modelling A Review","volume":"42","author":"Haines","year":"1990","journal-title":"J. Geomagn. Geoelectr."},{"key":"ref_11","unstructured":"Huber, P.J. (2004). Robust Statistics, John Wiley & Sons."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Coddington, E.A., Levinson, N., and Teichmann, T. (1956). Theory of Ordinary Differential Equations, McGraw-Hill Inc.","DOI":"10.1063\/1.3059875"},{"key":"ref_13","first-page":"7","article-title":"Applied comparisons between SCHA and R-SCHA regional modeling techniques","volume":"9","year":"2008","journal-title":"Geochem. Geophys. Geosyst."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2583","DOI":"10.1029\/JB090iB03p02583","article-title":"Spherical cap harmonic analysis","volume":"90","author":"Haines","year":"1985","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1111\/j.1365-246X.2008.03823.x","article-title":"A proposal for regional modelling at the Earth\u2019s surface, R-SCHA2D","volume":"174","year":"2008","journal-title":"Geophys. J. Int."},{"key":"ref_16","first-page":"B01102","article-title":"Revised spherical cap harmonic analysis (R-SCHA): Validation and properties","volume":"111","author":"Schott","year":"2006","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Blakely, R.J. (1996). Potential Theory in Gravity and Magnetic Applications, Cambridge University Press.","DOI":"10.1017\/CBO9780511549816"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"6339","DOI":"10.1029\/JA075i031p06339","article-title":"Non-uniqueness of the external geomagnetic field determined by surface intensity measurements","volume":"75","author":"Backus","year":"1970","journal-title":"J. Geophys. Res."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1637","DOI":"10.1007\/s11430-013-4784-1","article-title":"Regional gravity field modeling based on rectangular harmonic analysis","volume":"57","author":"Jiang","year":"2014","journal-title":"Sci. China Earth Sci."},{"key":"ref_20","unstructured":"Lanczos, C. (1988). Applied Analysis, Dover Publication, Inc."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s40623-020-01252-9","article-title":"The CHAOS-7 geomagnetic field model and observed changes in the South Atlantic Anomaly","volume":"72","author":"Finlay","year":"2020","journal-title":"Earth Planets Space"},{"key":"ref_22","unstructured":"Le Mouel, J. (1969). Sur la Distribution des Elements Magnetiques en France. [Ph.D. Thesis, University de Paris]."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s40623-016-0404-6","article-title":"Building the second version of the world digital magnetic anomaly map (WDMAM)","volume":"68","author":"Lesur","year":"2016","journal-title":"Earth Planets Space"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"e2021GL095147","DOI":"10.1029\/2021GL095147","article-title":"A spherical harmonic model of Earth\u2019s lithospheric magnetic field up to degree 1050","volume":"48","author":"Hulot","year":"2021","journal-title":"Geophys. Res. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Gailler, L., Labazuy, P., R\u00e9gis, E., Bontemps, M., Souriot, T., Bacques, G., and Carton, B. (2021). Validation of a new UAV magnetic prospecting tool for volcano monitoring and geohazard assessment. Remote Sens., 13.","DOI":"10.3390\/rs13050894"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1190\/1.1440416","article-title":"Additional comments on the analytic signal of two-dimensional magnetic bodies with polygonal cross-section","volume":"39","author":"Nabighian","year":"1974","journal-title":"Geophysics"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"104791","DOI":"10.1016\/j.jappgeo.2022.104791","article-title":"Research on aeromagnetic compensation of a multi-rotor UAV based on robust principal component analysis","volume":"206","author":"Qiao","year":"2022","journal-title":"J. Appl. Geophys."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/18\/4549\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:51:51Z","timestamp":1760129511000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/18\/4549"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9,15]]},"references-count":27,"journal-issue":{"issue":"18","published-online":{"date-parts":[[2023,9]]}},"alternative-id":["rs15184549"],"URL":"https:\/\/doi.org\/10.3390\/rs15184549","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,9,15]]}}}